Claire Holmberg
Professor Little
Applied Pre Calculus
2 December 2014
Blog Post 4: Be the
Professor
Completing the Square
Today, we will learn how to “complete the square” and the
purpose and reasons for completing the square.
We can complete the square to solve a Quadratic equation.
The process of completing the square is fairly simple if you
follow the same format each time.
Follow this format to complete the square to solve a
Quadratic equation:
1.
Move any loose numbers (numbers by themselves)
to the opposite (or zero) side of the equation.
2.
Take half of the x-term,
or the term that has an x with it, and square it. Add this square to both sides
of the equation.
3.
Then change the left side, or the side without the “loose” numbers, into
squared form. We squared the halved
number so that we could then change it into squared form. Also, add the
loose numbers together on the other side.
4.
Find the square root of each side. Use ± on the right side.
5.
Then solve for x. The ± will give you two answers.
Now we can put in numbers for a real example!!
Solve x2 + 6x –
7 = 0 by completing the square.
x2 + 6x
= 7
6/2 > 32 > 9
x2 + 6x +
9 = 7 + 9
(x +
3)2 = 16
x + 3 = ± 4
x =
– 3 ± 4
= – 3 – 4, –3 + 4
= –7, +1
= – 3 – 4, –3 + 4
= –7, +1
Conclusion:
If we
follow this format when completing the square, it is easy to find the solutions
for Quadratic equations!
This is awesome!
ReplyDeleteThe final example acted as a good way to rap everything up and show what you said in application!
ReplyDeleteclaire,
ReplyDeletenice job on explaining completing the square! sadly, i could not see your graphics, but your step by step explanations made it seem like i could see them. really like your conclusion! good job!
professor little